Industrial design using interpolatory discrete developable surfaces

Design using free-form developable surfaces plays an important role in the manufacturing industry. Currently most commercial systems can only support converting free-form surfaces into approximate developable surfaces. Direct design using developable surfaces by interpolating descriptive curves is much desired in industry. In this paper, by enforcing a propagation scheme and observing its nesting and recursive nature, a dynamic programming method is proposed for the design task of interpolating 3D boundary curves with a discrete developable surface. By using dynamic programming, the interpolatory discrete developable surface is obtained by globally optimizing an objective that minimizes tangent plane variations over a boundary triangulation. The proposed method is simple and effective when used in industry. Experimental results are presented that demonstrate its practicality and efficiency in industrial design.

► A method to directly design free-form developable shape is proposed. ► The surface is obtained by globally optimizing a tangent-variation objective. ► A dynamic programming method is used for the design task. ► A simple and easy-to-use sketching interface is developed.